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IRISSAK [1]
3 years ago
11

If devin has 3 times as many nickels as quarters and they have a combined value of 200 cents how many of each coin does he have

Mathematics
1 answer:
inysia [295]3 years ago
4 0

Devin has 15 nickel coins and 5 quarter coins.

Step-by-step explanation:

Total worth = 200 cents

1 nickel = 5 cents

1 quarter = 25 cents

Let,

Nickels = x

Quarters = y

According to given statement;

5x+25y=200    Eqn 1

x = 3y    Eqn 2

Putting x=3y in Eqn 1

5(3y)+25y=200\\15y+25y=200\\40y=200

Dividing both sides by 40

\frac{40y}{40}=\frac{200}{40}\\y=5

Putting y=5 in Eqn 2

x=3(5)\\x=15

Devin has 15 nickel coins and 5 quarter coins.

Keywords: linear equation, substitution method

Learn more about substitution method at:

  • brainly.com/question/4034547
  • brainly.com/question/4054269

#LearnwithBrainly

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Answer:

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Step-by-step explanation:

n+ 1 = 4(n-8)

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3 years ago
The Salk polio vaccine experiment in 1954 focused on the effectiveness of the vaccine in combating paralytic polio. Because it w
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Answer:

Step-by-step explanation:

Hello!

The variables of interest are:

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X₂: Number of cases of polio observed in kids that received the experimental vaccine.

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These two variables have a binomial distribution. The parameters of interest, the ones to compare, are the population proportions: p₁ vs p₂

You have to test if the population proportions of children who contracted polio in both groups are different: p₂ ≠ p₁

a)

H₀: p₂ = p₁

H₁: p₂ ≠ p₁

α: 0.05

Z= \frac{(p'_2-p'_1)-(p_2-p_1)}{\sqrt{p'[\frac{1}{n_1} +\frac{1}{n_2} ]} }

Sample proportion placebo p'₁= x₁/n₁= 110/201299= 0.0005

Sample proportion vaccine p'₂= x₂/n₂= 33/200745= 0.0002

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This test is two-tailed, using the critical value approach, you have to determine two critical values:

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Z_{1-\alpha /2}= Z_{0.975}= 1.96

Then if Z_{H_0} ≤ -1.96 or if Z_{H_0} ≥ 1.96, the decision is to reject the null hypothesis.

If -1.96 < Z_{H_0} < 1.96, the decision is to not reject the null hypothesis.

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b)

H₀: p₂ = p₁

H₁: p₂ ≠ p₁

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Z= \frac{(p'_2-p'_1)-(p_2-p_1)}{\sqrt{p'[\frac{1}{n_1} +\frac{1}{n_2} ]} }

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The only thing that changes alongside with the level of significance is the rejection region:

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c)

Remember the level of significance (probability of committing type I error) is the probability of rejecting a true null hypothesis. This means that the smaller this value is, the fewer chances you have of discarding the true null hypothesis. But as you know, you cannot just reduce this value to zero because, the smaller α is, the bigger β (probability of committing type II error) becomes.

Rejecting the null hypothesis using different values of α means that there is a high chance that you reached a correct decision (rejecting a false null hypothesis)

I hope this helps!

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